# An Image Segmentation Model with Transformed Total Variation

arXiv: https://arxiv.org/abs/2406.00571 · HTML: https://mlsanity.com/paper/2406.00571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 28 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 3 of 3)

- [Improving Network Slimming with Nonconvex Regularization](https://mlsanity.com/paper/2010.01242/) (2020)
- [A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity](https://mlsanity.com/paper/1504.02206/) (2015)
- [A Weighted Difference of Anisotropic and Isotropic Total Variation for Relaxed Mumford-Shah Color and Multiphase Image Segmentation](https://mlsanity.com/paper/2005.04401/) (2020)

## Abstract (arXiv)

Based on transformed ℓ1 regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TVp, 0<p<1. Inspired by its performance, we propose a TTV-regularized Mumford--Shah model with fuzzy membership function for image segmentation. To solve it, we design an alternating direction method of multipliers (ADMM) algorithm that utilizes the transformed ℓ1 proximal operator. Numerical experiments demonstrate that using TTV is more effective than classical TV and other nonconvex TV variants in image segmentation.